Number

1,040

1,040 is a composite number, even, a calendar year.

1,040 (one thousand forty) is an even 4-digit number. It is a composite number with 20 divisors, and factors as 2⁴ × 5 × 13. Its proper divisors sum to 1,564, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MXL and in binary, 10000010000.

Abundant Number Evil Number Gapful Number Harshad / Niven Pernicious Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

★ ★ ★ ★ ☆

6 notable facts · grade B

1,028 1,029 1,030 1,031 1,032 1,033 1,034 1,035 1,036 1,037 1,038 1,039 1,040 1,041 1,042 1,043 1,044 1,045 1,046 1,047 1,048 1,049 1,050 1,051 1,052

less more

Historical context — 1040 AD

Calendar year

Year 1040 (MXL) was a leap year starting on Tuesday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 1040
Ended on: Thursday
December 31, 1040
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 1040s
1040–1049
Century: 11th century
1001–1100
Millennium: 2nd millennium
1001–2000
Years ago: 986
986 years before 2026.

In other calendars

Hebrew: 4800 / 4801 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 431 / 432 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Metal zodiac:Dragon
Sexagenary cycle position 17 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1583 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 418 / 419 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1032 / 1033 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 962 / 961 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 5
Digit product: 0
Digital root: 5
Palindrome: No
Bit width: 11 bits
Reversed: 401
Recamán's sequence: a(4,339) = 1,040
Square (n²): 1,081,600
Cube (n³): 1,124,864,000
Divisor count: 20
σ(n) — sum of divisors: 2,604
φ(n) — Euler's totient: 384
Sum of prime factors: 26

Primality

Prime factorization: 2 ⁴ × 5 × 13

Nearest primes: 1,039 (−1) · 1,049 (+9)

Divisors & multiples

All divisors (20)

1 · 2 · 4 · 5 · 8 · 10 · 13 · 16 · 20 · 26 · 40 · 52 · 65 · 80 · 104 · 130 · 208 · 260 · 520 (half) · 1040

Aliquot sum (sum of proper divisors): 1,564

Factor pairs (a × b = 1,040)

1 × 1040

2 × 520

4 × 260

5 × 208

8 × 130

10 × 104

13 × 80

16 × 65

20 × 52

26 × 40

First multiples

1,040 · 2,080 (double) · 3,120 · 4,160 · 5,200 · 6,240 · 7,280 · 8,320 · 9,360 · 10,400

Sums & aliquot sequence

As a sum of two squares: 4² + 32² = 16² + 28²

As consecutive integers: 206 + 207 + 208 + 209 + 210 74 + 75 + … + 86 17 + 18 + … + 48

Aliquot sequence: 1,040 → 1,564 → 1,460 → 1,648 → 1,576 → 1,394 → 874 → 566 → 286 → 218 → 112 → 136 → 134 → 70 → 74 → 40 → 50 — unresolved within range

Continued fraction of √n

√1,040 = [32; (4, 64)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: one thousand forty
Ordinal: 1040th
Roman numeral: MXL
Binary: 10000010000
Octal: 2020
Hexadecimal: 0x410
Base64: BBA=
One's complement: 64,495 (16-bit)
Scientific notation: 1.04 × 10³
As a duration: 1,040 s = 17 minutes, 20 seconds

In other bases

ternary (3) 1102112

quaternary (4) 100100

quinary (5) 13130

senary (6) 4452

septenary (7) 3014

nonary (9) 1375

undecimal (11) 866

duodecimal (12) 728

tridecimal (13) 620

tetradecimal (14) 544

pentadecimal (15) 495

As an angle

1,040° = 2 × 360° + 320°

320° ≈ 5.585 rad

Compass bearing: NW (northwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋
Egyptian hieroglyphic: 𓆼𓎆𓎆𓎆𓎆
Greek (Milesian): ͵αμʹ
Mayan (base 20): 𝋢·𝋬·𝋠
Chinese: 一千零四十
Chinese (financial): 壹仟零肆拾

In other modern scripts

Eastern Arabic ١٠٤٠ Devanagari १०४० Bengali ১০৪০ Tamil ௧௦௪௦ Thai ๑๐๔๐ Tibetan ༡༠༤༠ Khmer ១០៤០ Lao ໑໐໔໐ Burmese ၁၀၄၀

Digit at this position in famous constants

π — Pi (π): Digit 1,040 = 9
e — Euler's number (e): Digit 1,040 = 2
φ — Golden ratio (φ): Digit 1,040 = 0
√2 — Pythagoras's (√2): Digit 1,040 = 7
ln 2 — Natural log of 2: Digit 1,040 = 0
γ — Euler-Mascheroni (γ): Digit 1,040 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1040, here are decompositions:

7 + 1033 = 1040
19 + 1021 = 1040
31 + 1009 = 1040
43 + 997 = 1040
73 + 967 = 1040
103 + 937 = 1040
157 + 883 = 1040
163 + 877 = 1040

Showing the first eight; more decompositions exist.

Unicode codepoint

Cyrillic Capital Letter A

U+0410

Uppercase letter (Lu)

UTF-8 encoding: D0 90 (2 bytes).

Lookup U+0410 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000410

RGB(0, 4, 16)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.4.16.

Address: 0.0.4.16
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.4.16

Unspecified address (0.0.0.0/8) — "this network" placeholder.

Musical pitch

Heard as a frequency, 1,040 Hz is closest to:

Concert pitch (A4 = 440 Hz): C6 (1046.5 Hz, -11¢)
Scientific pitch (C4 = 256 Hz): C6 (1024 Hz, +27¢)
Baroque pitch (A4 = 415 Hz): C♯6 (1045.7 Hz, -10¢)

Position in π

The digit sequence 1040 first appears in π at position 1,270 of the decimal expansion (the 1,270ordinal-suffix:th digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.

Look up 1040 on Pi Search ↗